Question

What is the area of the polygon? The lengths is 12, 12, 5, 5 and 6.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the area of a polygon, you can use various methods depending on the type of polygon. In this case, we can divide the polygon into two triangles and use the formula for finding the area of a triangle.

We can see that the polygon can be divided into two triangles with side lengths of 12, 12, and 5, and side lengths of 5, 6, and 12.

For the first triangle:
s = (12 + 12 + 5) / 2 = 29 / 2 = 14.5
Area = √[14.5(14.5-12)(14.5-12)(14.5-5)]
Area = √[14.5(2.5)(2.5)(9.5)]
Area = √[14.5(5)(5)(9.5)]
Area = √[14.5(25)(9.5)]
Area = √3462.5
Area = 58.86 (approximately)

For the second triangle:
s = (5 + 6 + 12) / 2 = 23 / 2 = 11.5
Area = √[11.5(11.5-5)(11.5-6)(11.5-12)]
Area = √[11.5(6.5)(5.5)(-0.5)]
Area = √[11.5(35.75)(-0.5)]
Area = √[11.5(-21.5)]
Area = √-247.75
Area = 0 (approximately)

Therefore, the total area of the polygon is approximately 58.86.